Problem: Express this product in scientific notation: $(9.20\times 10^{-2})\times (4.00\times 10^{4})$
Explanation: Start by collecting like terms together. $= (9.20\times 4.00) \times (10^{-2}\times 10^{4})$ When multiplying exponents with the same base, add the powers together. $= 36.8 \times 10^{-2\,+\,4}$ $= 36.8 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $36.8$ is the same as $3.680 \times 10$ $ = {3.680 \times 10} \times 10^{2} $ $= 3.680\times 10^{3}$